According to "API Enterprise 2.5":

All API endpoints—except Management Console API endpoints—are prefixed with the following URL:

https://hostname/api/v3/

But you need to authenticate:

Authentication

Your Enterprise installation's API endpoints accept the same authentication methods as the GitHub.com API. Specifically, you can authenticate yourself with OAuth tokens (which can be created using the Authorizations API) or basic authentication.

Every Enterprise API endpoint is only accessible to GitHub Enterprise site administrators, with the exception of the Management Console API, which is only accessible via the Management Console password.

First register for one here and there is a guide for it: (https://docs.github.com/en/integrations/concepts/github-developer-program). I think they give you the key details and the links that you would need to continue your project. However, that's only if your business doesn't have one yet. If your business already has an established enterprise instance, the API URL is already generated based on your company's domain hosting layout:

Self-Hosted/On-Premise (e.g., github.company.com): Your REST API URL is https://github.company.com/api/v3
Standard Public Cloud (e.g., github.com/company): Your REST API URL is https://api.github.com
Dedicated Subdomain (e.g., company.ghe.com): Your REST API URL is https://api.company.ghe.com

You won't need to wait on GitHub to generate a link. You just need to create a Personal Access Token (PAT) or a GitHub App integration within your existing enterprise settings to start making requests.

https://docs.github.com/en/rest?apiVersion=2022-11-28 is correct.

Please a have look the left sidebar REST API reference

For each user, you receive a url for more details api. In your example, the first user has

{
  ...
  "url": "https://api.github.com/users/mojombo",
  ...
},

Or just follow the schema https://api.github.com/users/{username} If you call this url (try), you will get the twitter account and more.

{
  "login": "mojombo",
  "id": 1,
  "node_id": "MDQ6VXNlcjE=",
  "avatar_url": "https://avatars.githubusercontent.com/u/1?v=4",
  "gravatar_id": "",
  "url": "https://api.github.com/users/mojombo",
  "html_url": "https://github.com/mojombo",
  "followers_url": "https://api.github.com/users/mojombo/followers",
  "following_url": "https://api.github.com/users/mojombo/following{/other_user}",
  "gists_url": "https://api.github.com/users/mojombo/gists{/gist_id}",
  "starred_url": "https://api.github.com/users/mojombo/starred{/owner}{/repo}",
  "subscriptions_url": "https://api.github.com/users/mojombo/subscriptions",
  "organizations_url": "https://api.github.com/users/mojombo/orgs",
  "repos_url": "https://api.github.com/users/mojombo/repos",
  "events_url": "https://api.github.com/users/mojombo/events{/privacy}",
  "received_events_url": "https://api.github.com/users/mojombo/received_events",
  "type": "User",
  "site_admin": false,
  "name": "Tom Preston-Werner",
  "company": "@chatterbugapp, @redwoodjs, @preston-werner-ventures ",
  "blog": "http://tom.preston-werner.com",
  "location": "San Francisco",
  "email": null,
  "hireable": null,
  "bio": null,
  "twitter_username": "mojombo",
  "public_repos": 62,
  "public_gists": 62,
  "followers": 22447,
  "following": 11,
  "created_at": "2007-10-20T05:24:19Z",
  "updated_at": "2021-03-18T22:50:53Z"
}

You'll need to use the GraphQL API, and you're looking for the homepageUrl field under a given repo. For example, the query below will give all public repositories for a given user, and for each repository, it will give its name, description, and homepage:

query MyQuery {
  repositoryOwner(login: "username") {
    repositories(orderBy: {field: CREATED_AT, direction: DESC}, first: 100, privacy: PUBLIC) {
      nodes {
        name
        description
        homepageUrl
      }
    }
  }
}

Unlike the REST api, the GraphQL api requires authentication. You can tinker around with the query here.